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<p><code>#include &lt;<a class="el" href="cayley__graph_8h_source.html">cayley_graph.h</a>&gt;</code></p>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcCayleyGrf_1_1cColourEdgesVis.html">cColourEdgesVis</a></td></tr>
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typedef G::ElementType&#160;</td><td class="memItemRight" valign="bottom"><b>ElemType</b></td></tr>
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typedef boost::adjacency_list<br class="typebreak"/>
&lt; boost::vecS, boost::vecS, <br class="typebreak"/>
boost::bidirectionalS, <br class="typebreak"/>
boost::no_property, std::pair<br class="typebreak"/>
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typedef boost::graph_traits<br class="typebreak"/>
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typedef boost::graph_traits<br class="typebreak"/>
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typedef boost::graph_traits<br class="typebreak"/>
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typedef boost::graph_traits<br class="typebreak"/>
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typedef boost::graph_traits<br class="typebreak"/>
&lt; Graph &gt;::in_edge_iterator&#160;</td><td class="memItemRight" valign="bottom"><b>inEdge</b></td></tr>
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Public Member Functions</h2></td></tr>
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&#160;</td><td class="memItemRight" valign="bottom"><b>cCayleyGrf</b> (std::vector&lt; ElemType &gt; &amp;elements, std::vector&lt; ElemType &gt; &amp;generators)</td></tr>
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&#160;</td><td class="memItemRight" valign="bottom"><b>cCayleyGrf</b> (G &amp;group)</td></tr>
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void&#160;</td><td class="memItemRight" valign="bottom"><b>initGraph</b> (const std::vector&lt; ElemType &gt; &amp;elements, const std::vector&lt; ElemType &gt; &amp;generators)</td></tr>
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&#160;</td><td class="memItemRight" valign="bottom"><b>cCayleyGrf</b> (const <a class="el" href="classcCayleyGrf.html">cCayleyGrf</a> &amp;graph)</td></tr>
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<a class="el" href="classcCayleyGrf.html">cCayleyGrf</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><b>operator=</b> (const <a class="el" href="classcCayleyGrf.html">cCayleyGrf</a> &amp;graph)</td></tr>
<tr class="separator:a31a02f7a0e7702fe953409f7f82888be"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a4a0ff02aa7bb9d556456b34e9f66f3d9"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcCayleyGrf.html#a4a0ff02aa7bb9d556456b34e9f66f3d9">BuildGraph</a> ()</td></tr>
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<tr class="memitem:a8517436f6101a294fa7f30355efaa196"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcCayleyGrf.html#a8517436f6101a294fa7f30355efaa196">BuildDefRelations</a> ()</td></tr>
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const std::vector<br class="typebreak"/>
&lt; <a class="el" href="classcGroupRelation.html">cGroupRelation</a> &gt; &amp;&#160;</td><td class="memItemRight" valign="bottom"><b>GetDefRelations</b> () const </td></tr>
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<tr class="memitem:aeb4d8533b65921ca63fdaaf4516f92f6"><td class="memItemLeft" align="right" valign="top">Graph *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcCayleyGrf.html#aeb4d8533b65921ca63fdaaf4516f92f6">GetGraph</a> () const </td></tr>
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Private Member Functions</h2></td></tr>
<tr class="memitem:a1d6153e03d163ea10242b4088091c705"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcCayleyGrf.html#a1d6153e03d163ea10242b4088091c705">Add_DefRelation</a> (const Edge &amp;edge, std::vector&lt; std::size_t &gt; &amp;spanning_tree)</td></tr>
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<tr class="memitem:a2598371d6a962b027539109023bc65b5"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcCayleyGrf.html#a2598371d6a962b027539109023bc65b5">TraceRelations</a> ()</td></tr>
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Private Attributes</h2></td></tr>
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std::vector&lt; ElemType &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>m_Elements</b></td></tr>
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std::vector&lt; ElemType &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>m_Generators</b></td></tr>
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Graph *&#160;</td><td class="memItemRight" valign="bottom"><b>m_Graph</b></td></tr>
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std::vector&lt; <a class="el" href="classcGroupRelation.html">cGroupRelation</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>m_DefRelations</b></td></tr>
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Friends</h2></td></tr>
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std::ostream &amp;&#160;</td><td class="memItemRight" valign="bottom"><b>operator&lt;&lt;</b> (std::ostream &amp;out, const <a class="el" href="classcCayleyGrf.html">cCayleyGrf</a> &amp;graph)</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template&lt;typename G&gt;<br/>
class cCayleyGrf&lt; G &gt;</h3>

<p>implementation of a Cayley Graph(used to represent an abbreviated multiplication table) template must be instantiated with a group type uses Boost Graph Library for graph representation as an adjacency list </p>
</div><h2 class="groupheader">Member Function Documentation</h2>
<a class="anchor" id="a1d6153e03d163ea10242b4088091c705"></a>
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<div class="memtemplate">
template&lt;typename G &gt; </div>
<table class="mlabels">
  <tr>
  <td class="mlabels-left">
      <table class="memname">
        <tr>
          <td class="memname">void <a class="el" href="classcCayleyGrf.html">cCayleyGrf</a>&lt; G &gt;::Add_DefRelation </td>
          <td>(</td>
          <td class="paramtype">const Edge &amp;&#160;</td>
          <td class="paramname"><em>edge</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">std::vector&lt; std::size_t &gt; &amp;&#160;</td>
          <td class="paramname"><em>spanning_tree</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
  </td>
  <td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">private</span></span>  </td>
  </tr>
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<p>add the defining relation corresponding to the given vertex to the set of defining relations </p>

<p><div class="dynheader">
Here is the call graph for this function:</div>
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<div class="center"><img src="classcCayleyGrf_a1d6153e03d163ea10242b4088091c705_cgraph.png" border="0" usemap="#classcCayleyGrf_a1d6153e03d163ea10242b4088091c705_cgraph" alt=""/></div>
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</p>

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<div class="memtemplate">
template&lt;typename G &gt; </div>
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  <td class="mlabels-left">
      <table class="memname">
        <tr>
          <td class="memname">void <a class="el" href="classcCayleyGrf.html">cCayleyGrf</a>&lt; G &gt;::BuildDefRelations </td>
          <td>(</td>
          <td class="paramname"></td><td>)</td>
          <td></td>
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<p>extract the set of defining relations using Cannon's algorithm with one stage see Butler - "Fundamental Algorithms for permutation groups" </p>

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<p>builds the Cayle graph as and adjacency list: the nodes are the indexes of the elements, the edges are the indexes of the generators Complexity: O(n*m), where n is the number of generators and m the number of elements </p>

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<p>returns the underlying graph representation (adjacency list) </p>

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<p>trace the relations around all the nodes in the graph and colour the appropriate edges (if loop contains exactly one uncoloured edge) </p>

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<hr/>The documentation for this class was generated from the following file:<ul>
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